Abstract The excitation of a linear quantum oscillator (LQO) upon a collision with a charged particle moving in a rectilinear trajectory is analyzed. The probability and the cross section of the process are calculated beyond the framework of perturbation theory for different charges of the incident particle, including multiply charged ions. The excitation between the LQO stationary states, as well as total excitation from the ground state, are considered. The characteristic features of the process depending on the problem parameters are analyzed.Abstract The excitation of a linear quantum oscillator (LQO) upon a collision with a charged particle moving in a rectilinear trajectory is analyzed. The probability and the cross section of the process are calculated beyond the framework of perturbation theory for different charges of the incident particle, including multiply charged ions. The excitation between the LQO stationary states, as well as total excitation from the ground state, are considered. The characteristic features of the process depending on the problem parameters are analyzed.

Journal of Experimental and Theoretical PhysicsMay 1, 20211 citation

Oscillations in an Ensemble of Noninteracting Oscillators

Mikhail I. Rabinovich, D. I. Trubet︠s︡kov

Springer eBooksJan 1, 19890 citations

Linear Oscillator with Time-Dependent Frequency

Walter Dittrich, Martin Reuter

Graduate texts in physicsOct 8, 20150 citations

Wave Packet Solutions of the Schrdinger Equation for Simple Harmonic Oscillator

Dong Shao

By solving exactly the time dependent Schrdinger equation for simple harmonic oscillator, we have obtained respectively the wave packet solutions associated with the displaced ground state and the displaced excited eigenstates, and then demonstrated the centroid of the wave packet oscillates according to the classical law and that the wave packet form remains unchanged. For simple harmonic oscillator with the force constant depending on time the wave packets with the same structures as that of the usual simple harmonic oscillator can still be found to move in such a way that the centroids move according to the classical law, but their wave packets may deform in time. Depending on how the force constant varies with time, the wave packets can spread, contract or pulsate.By solving exactly the time dependent Schrdinger equation for simple harmonic oscillator, we have obtained respectively the wave packet solutions associated with the displaced ground state and the displaced excited eigenstates, and then demonstrated the centroid of the wave packet oscillates according to the classical law and that the wave packet form remains unchanged. For simple harmonic oscillator with the force constant depending on time the wave packets with the same structures as that of the usual simple harmonic oscillator can still be found to move in such a way that the centroids move according to the classical law, but their wave packets may deform in time. Depending on how the force constant varies with time, the wave packets can spread, contract or pulsate.

Journal of Sichuan Teachers CollegeJan 1, 20020 citations

Linear Oscillator with Time-Dependent Frequency

Walter Dittrich, Martin Reuter

Springer eBooksJan 1, 20170 citations

R -matrix approach to collision processes: Study of the threshold behavior of γ + He → He +(2s)+e− or He +(2p)+e−

Hao Xu, Robin Shakeshaft

We report on a study of one-photon single ionization of He( $1{s}^{2}$ ) accompanied by excitation to He ${}^{+}(2s)$ or He ${}^{+}(2p)$ for photon energies at, and up to a few eV above, the excitation threshold. We find, both numerically and analytically, that as the photon energy approaches threshold from above the photoionization cross section turns sharply at about 200 meV and has a cusp at threshold. The cusp is associated with the adiabatic transfer of population between the $2s$ and $2p$ bound states of the ion. The photoelectron's electric field induces an energy splitting between the otherwise degenerate $2s$ and $2p$ states, and consequently the $2s$ and $2p$ populations oscillate with a period defined by this energy splitting. The number of oscillations is almost independent of the photoelectron's asymptotic speed $v$ since over most of its outward journey the photoelectron moves with a speed much larger than $v$ . However, on the last leg of its journey, after it has slowed down sufficiently in the Coulomb field of the ion, the photoelectron does move with an almost constant speed $v$ . On this last leg the energy splitting is so small that there is insufficient time for $2s$ and $2p$ populations to undergo a full oscillation; rather, the (equal and opposite) changes in the $2s$ and $2p$ populations are proportional to $v$ (i.e., to the square root of the excess photoelectron energy, which gives rise to a cusp).We report on a study of one-photon single ionization of He($1{s}^{2}$) accompanied by excitation to He${}^{+}(2s)$ or He${}^{+}(2p)$ for photon energies at, and up to a few eV above, the excitation threshold. We find, both numerically and analytically, that as the photon energy approaches threshold from above the photoionization cross section turns sharply at about 200 meV and has a cusp at threshold. The cusp is associated with the adiabatic transfer of population between the $2s$ and $2p$ bound states of the ion. The photoelectron's electric field induces an energy splitting between the otherwise degenerate $2s$ and $2p$ states, and consequently the $2s$ and $2p$ populations oscillate with a period defined by this energy splitting. The number of oscillations is almost independent of the photoelectron's asymptotic speed $v$ since over most of its outward journey the photoelectron moves with a speed much larger than $v$. However, on the last leg of its journey, after it has slowed down sufficiently in the Coulomb field of the ion, the photoelectron does move with an almost constant speed $v$. On this last leg the energy splitting is so small that there is insufficient time for $2s$ and $2p$ populations to undergo a full oscillation; rather, the (equal and opposite) changes in the $2s$ and $2p$ populations are proportional to $v$ (i.e., to the square root of the excess photoelectron energy, which gives rise to a cusp).

Physical Review AJan 31, 20113 citations

We report on a study of one-photon single ionization of He(

1{s}^{2}

) accompanied by excitation to He

{}^{+}(2s)

or He

{}^{+}(2p)

for photon energies at, and up to a few eV above, the excitation threshold. We find, both numerically and analytically, that as the photon energy approaches threshold from above the photoionization cross section turns sharply at about 200 meV and has a cusp at threshold. The cusp is associated with the adiabatic transfer of population between the

2s

and

2p

bound states of the ion. The photoelectron's electric field induces an energy splitting between the otherwise degenerate

2s

and

2p

states, and consequently the

2s

and

2p

populations oscillate with a period defined by this energy splitting. The number of oscillations is almost independent of the photoelectron's asymptotic speed

v

since over most of its outward journey the photoelectron moves with a speed much larger than

v

. However, on the last leg of its journey, after it has slowed down sufficiently in the Coulomb field of the ion, the photoelectron does move with an almost constant speed

v

. On this last leg the energy splitting is so small that there is insufficient time for

2s

and

2p

populations to undergo a full oscillation; rather, the (equal and opposite) changes in the

2s

and

2p

populations are proportional to

v

(i.e., to the square root of the excess photoelectron energy, which gives rise to a cusp).